1. Chapter 23: Dark Matter & The Fate Of The Universe

2. What is Dark Matter? Recall the rotation curve of the Milky Way Galaxy. atomic H clouds beyond our Sun orbit faster than predicted by Kepler’s Law atomic H clouds beyond our Sun orbit faster than predicted by Kepler’s Law most of the Galaxy’s light comes from stars closer to the center than the Sun most of the Galaxy’s light comes from stars closer to the center than the Sun There are only two possible explanations for this: we do not understand gravity on galaxy-size scales the H gas velocities are caused by the gravitational attraction of unseen matter…called dark matter If we trust our theory of gravity... there may be 10 times more dark than luminous matter in our Galaxy luminous matter is confined to the disk dark matter is found in the halo and far beyond the luminous disk

3. Determining Mass Distribution In Spiral Galaxies In Spiral Galaxies measure the Doppler shift of the 21-cm radio line at various radial distances measure the Doppler shift of the 21-cm radio line at various radial distances construct a rotation curve of the atomic Hydrogen gas (beyond visible disk) construct a rotation curve of the atomic Hydrogen gas (beyond visible disk) calculate the enclosed mass using Kepler’s Law calculate the enclosed mass using Kepler’s Law

4. Determining Mass Distribution Rotation curves of spirals… Rotation curves of spirals… are flat at large distances from their centers are flat at large distances from their centers indicates that (dark) matter is distributed far beyond disk indicates that (dark) matter is distributed far beyond disk In Elliptical Galaxies there is no gas measure the average orbital speeds of stars at various distances use broadened absorption lines Results indicate that dark matter lies beyond the visible galaxy. we can not measure the total amount of dark matter, since we can see only the motions of stars

5. Mass-to-Light Ratio… …is the mass of a galaxy divided by its luminosity. we measure both mass [M  ] and luminosity [L  ] in Solar units we measure both mass [M  ] and luminosity [L  ] in Solar units Within the orbit of the Sun, M/L = 6 M  / L  for the Milky Way this is typical for the inner regions of most spiral galaxies this is typical for the inner regions of most spiral galaxies for inner regions of elliptical galaxies, M/L = 10 M  / L  for inner regions of elliptical galaxies, M/L = 10 M  / L  not surprising since ellipticals contain dimmer stars not surprising since ellipticals contain dimmer stars However, when we include the outer regions of galaxies… M/L increases dramatically M/L increases dramatically for entire spirals, M/L can be as high as 50 M  / L  for entire spirals, M/L can be as high as 50 M  / L  dwarf galaxies can have even higher M/L dwarf galaxies can have even higher M/L Thus we conclude that most matter in galaxies are not stars. the amount of M/L over 6 M  / L  is the amount of dark matter the amount of M/L over 6 M  / L  is the amount of dark matter

6. Measuring the Mass of a Cluster There are three independent ways to measure galaxy cluster mass: There are three independent ways to measure galaxy cluster mass: 1. measure the speeds and positions of the galaxies within the cluster 2. measure the temperature and distribution of the hot gas between the galaxies 3. observe how clusters bend light as gravitational lenses Orbiting Galaxies This method was pioneered by Fritz Zwicky. assume the galaxies orbit about the cluster center measure the orbital velocities of the galaxies measure each galaxy’s distance from the center apply Kepler’s Law to calculate mass of cluster Zwicky found huge M/L ratios for clusters. his proposals of dark matter were met with skepticism in the 1930s Fritz Zwicky

7. Measuring the Mass of a Cluster Measuring galaxy orbits is not straightforward. Measuring galaxy orbits is not straightforward. we can only measure radial velocity we can only measure radial velocity must average all radial velocities to get the cosmological redshift (CR) must average all radial velocities to get the cosmological redshift (CR) subtract CR from each velocity subtract CR from each velocity Intracluster Medium is the hot (10 7 –10 8 K) gas between the cluster galaxies this gas emits X-rays from the X-ray spectrum, we can calculate the temperature this tells us the average speed of the gas particles again, we can estimate mass Coma cluster of galaxies (optical) (X-ray)

8. Measuring the Mass of a Cluster This is a gravitational lens. Einstein’s Theory of Relativity states that massive objects distort spacetime. a massive cluster will bend the path of light which approaches it (like a lens) a massive cluster will bend the path of light which approaches it (like a lens) the blue arcs are the lensed images of a galaxy which is behind the cluster the blue arcs are the lensed images of a galaxy which is behind the cluster The angle at which the light is bent depends on the mass of the cluster. by analyzing lensed images, we can calculate cluster mass All previous methods for finding mass depended on Newton’s Law of Gravity. this method uses a different theory of gravity

9. Measuring the Mass of a Cluster The cluster masses which are measured by all three of these independent methods agree: M/L for most galaxy clusters is greater than 100 M  / L  M/L for most galaxy clusters is greater than 100 M  / L  galaxy clusters contain far more mass in dark matter than in stars galaxy clusters contain far more mass in dark matter than in stars

10. Some observations of the universe are very difficult to explain without dark matter. Some observations of the universe are very difficult to explain without dark matter.

11. What is Dark Matter Made Of? Dark matter could be made out of protons, neutrons, & electrons. so-called “ordinary” matter, the same matter we are made up of so-called “ordinary” matter, the same matter we are made up of if this is so, then the only thing unusual about dark matter is that it is dim if this is so, then the only thing unusual about dark matter is that it is dim However, some or all of dark matter could be made of particles which we have yet to discover. this would find this to be “extraordinary” matter this would find this to be “extraordinary” matter Physicists like to call ordinary matter baryonic matter. protons & neutrons are called baryons protons & neutrons are called baryons They call extraordinary matter nonbaryonic matter.

12. An Ordinary Matter Candidate Our Galactic halo should contain baryonic matter which is dark: low-mass M dwarfs, brown dwarfs, and Jovian-sized planets low-mass M dwarfs, brown dwarfs, and Jovian-sized planets they are too faint to be seen at large distances they are too faint to be seen at large distances they have been called “MAssive Compact Halo Objects” or MACHOs they have been called “MAssive Compact Halo Objects” or MACHOs We detect them if they pass in front of a star where they… gravitationally lens the star’s light the star gets much brighter for a few days to weeks we can measure the MACHO’s mass These events occur to only one in a million stars per year. must monitor huge numbers of stars # of MACHOs detected so far does not account for the Milky Way’s dark matter

13. An Extraordinary Matter Candidate We have already studied a nonbaryonic form of matter: the neutrino…detected coming from the Sun the neutrino…detected coming from the Sun neutrinos interact with other particles through only two of the natural forces: neutrinos interact with other particles through only two of the natural forces: gravity gravity weak force (hence we say they are “weakly interacting”) weak force (hence we say they are “weakly interacting”) their masses are so low & speeds so high, they will escape the gravitational pull of a galaxy…they can not account for the dark matter observed their masses are so low & speeds so high, they will escape the gravitational pull of a galaxy…they can not account for the dark matter observed But what if there existed a massive weakly interacting particle? physicists call them “Weakly Interacting Massive Particles” or WIMPs physicists call them “Weakly Interacting Massive Particles” or WIMPs these particles are theoretical; they have not yet been discovered these particles are theoretical; they have not yet been discovered they would be massive enough to exert gravitational influence they would be massive enough to exert gravitational influence they would emit no electromagnetic radiation (light) or be bound to any charged matter which could emit light they would emit no electromagnetic radiation (light) or be bound to any charged matter which could emit light as weakly interacting particles, they would not collapse with a galaxy’s disk as weakly interacting particles, they would not collapse with a galaxy’s disk yet they would remain gravitationally bound in the galaxy’s halo yet they would remain gravitationally bound in the galaxy’s halo

14. The Growth of Structure At close range, gravitational attraction overcomes the Hubble expansion. we see this in a galaxy’s peculiar velocity we see this in a galaxy’s peculiar velocity although the Universe as a whole expands, individual galaxies attract one another although the Universe as a whole expands, individual galaxies attract one another peculiar velocity is a galaxy’s deviation from the Hubble Law peculiar velocity is a galaxy’s deviation from the Hubble Law can measure it for galaxies out to 3 x 10 8 ly can measure it for galaxies out to 3 x 10 8 ly We project that Universal structure began with slight enhancements in the density of matter in the early Universe. these regions collapsed into protogalactic clouds to form galaxies individual galaxies fell in towards one another to form clusters individual clusters are now congregating to form superclusters These “collapses” against Universal expansion are facilitated by dark matter.

15. Large Scale Structure of the Universe On scales of 10 8 ly, galaxies are distributed in gigantic chains and sheets surrounding great voids. the chains come from the initial regions of density enhancement the chains come from the initial regions of density enhancement the voids come from the initial regions of density depletion the voids come from the initial regions of density depletion On scales of several x 10 9 ly, galaxies appear evenly distributed. slice of the Universe out to 7 x 10 8 lyslice of the Universe out to 4 x 10 9 ly

16. Maps of galaxy positions reveal extremely large structures: superclusters and voids. Maps of galaxy positions reveal extremely large structures: superclusters and voids.

17. Time in billions of years 0.5 2.25.98.613.7 Size of expanding box in millions of light-years 13 357093140 Models show that gravity of dark matter pulls mass into denser regions—the universe grows lumpier with time. Models show that gravity of dark matter pulls mass into denser regions—the universe grows lumpier with time.

18. Models show that gravity of dark matter pulls mass into denser regions—universe grows lumpier with time. Models show that gravity of dark matter pulls mass into denser regions—universe grows lumpier with time.

19. Structures in galaxy maps look very similar to the ones found in models in which dark matter is WIMPs. Structures in galaxy maps look very similar to the ones found in models in which dark matter is WIMPs.

20. The Critical Density We have seen that gravitational attraction between galaxies can overcome the expansion of the Universe in localized regions. how strong must gravity be to stop the entire Universe from expanding? how strong must gravity be to stop the entire Universe from expanding? it depends on the total mass density of the Universe it depends on the total mass density of the Universe We refer to the mass density required for this gravitational pull to equal the kinetic energy of the Universe as the critical density. if mass < critical density, the Universe will expand forever if mass < critical density, the Universe will expand forever if mass > critical density, the Universe will stop expanding and then contract if mass > critical density, the Universe will stop expanding and then contract The value of H o tells us the current kinetic energy of the Universe. this being known, the critical density is 10 –29 g / cm 3 this being known, the critical density is 10 –29 g / cm 3 all the luminous matter that we observe accounts for < 1% of critical density all the luminous matter that we observe accounts for < 1% of critical density for dark matter to stop Universal expansion, the average M/L of the Universe would have to be 1,000 M  / L  … a few times greater than clusters for dark matter to stop Universal expansion, the average M/L of the Universe would have to be 1,000 M  / L  … a few times greater than clusters This line of research suggests the Universe will expand forever!

21. Does Gravity alone Influence the Expansion? Recent observations of white dwarf supernovae in very distant galaxies have yielded unexpected results. remember, white dwarf supernovae make very good standard candlesthe supernovae are apparently fainter than predicted for their redshifts remember, white dwarf supernovae make very good standard candlesthe supernovae are apparently fainter than predicted for their redshifts At a given cosmological redshift galaxies should be closer to us… i.e. shorter lookback time …for greater Universal mass densities these supernova are farther back in time than even the models for an ever- expanding (coasting) Universe predict This implies that the Universal expansion is accelerating! there must be an as yet unknown force which repels the galaxies a dark energy

22. The brightness of distant white dwarf supernovae tells us how much the universe has expanded since they exploded. The brightness of distant white dwarf supernovae tells us how much the universe has expanded since they exploded.

23. Four Models for the Future of the Universe 1. Recollapsing Universe: the expansion will someday halt and reverse 2. Critical Universe: will not collapse, but will expand more slowly with time 3. Coasting Universe: will expand forever with little slowdown 4. Accelerating Universe*: the expansion will accelerate with time *currently favored *currently favored

24. © 2014 Pearson Education, Inc. Contents of Universe "Ordinary" matter: ~ 4.4% "Ordinary" matter: ~ 4.4% Ordinary matter inside stars: ~ 0.6% Ordinary matter inside stars: ~ 0.6% Ordinary matter outside stars: ~ 3.8% Ordinary matter outside stars: ~ 3.8% Dark matter: ~ 23% Dark matter: ~ 23% Dark energy: ~ 73% Dark energy: ~ 73%

25. The eventual fate of the universe depends upon the rate of the acceleration of the expansion. The eventual fate of the universe depends upon the rate of the acceleration of the expansion. If the universe does not end in a Big Rip, it should keep expanding for a very long time. (Forever?) If the universe does not end in a Big Rip, it should keep expanding for a very long time. (Forever?) All matter will eventually end up as part of black holes, which will, if Stephen Hawking is right, will eventually evaporate. All matter will eventually end up as part of black holes, which will, if Stephen Hawking is right, will eventually evaporate. The Fate of the Universe